z-prime gamma submodule of gamma modules

Let r be a γ-ring and ∂ be an rγ-module. a proper rγ-submodule. t of an rγ-module ∂ is called z-prime rγ-submodule if for each t ∈ ∂, γ ∈ γ and f ∈ ∂∗ = homrγ (∂, r), f(t)γt ∈ t implies that either t ∈ t or f(t) ∈ [t :rγ ∂]. the purpose of this paper is to introduce interesting theorems and properties of z- prime rγ-submodule of rγ-module and the relation of z-prime rγ-submodule, which represents of generalization z-prime r-submodule of r-module.